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5. Assume that the graph below is the graph of the derivative $f_{?}(x)$ of a function $f(x)$. (a) Determine the intervals where the function $f(x)$ is increasing/decreasing. (b) Determine the intervals where $f(x)$ is concave up/down. (c) Using parts (a) and (b), determine whether the function $f$ is increasing or decreasing and whether it is concave up or down at $x=?1$. (d) Do the part (c) for $x=?4$. Extra Credit. Determine the values of the coefficients $a,b,c$, and $d$ so that the cubic function $f(x)=ax_{3}+bx_{2}+cx+d$ has a local maximum of 7 at -1 and a local minimum of -20 at 2 .

(a) The function is increasing wherever its derivative is positive, and decreasing wherever its derivative is negative. From the graph, we see that th

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